\[ \cos (x) y'(x)+y(x)+(\sin (x)+1) \cos (x)=0 \] ✓ Mathematica : cpu = 0.0556487 (sec), leaf count = 53
\[\left \{\left \{y(x)\to c_1 e^{-2 \tanh ^{-1}\left (\tan \left (\frac {x}{2}\right )\right )}+e^{-2 \tanh ^{-1}\left (\tan \left (\frac {x}{2}\right )\right )} \left (\sin (x)+4 \log \left (\cos \left (\frac {x}{2}\right )-\sin \left (\frac {x}{2}\right )\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.105 (sec), leaf count = 23
\[ \left \{ y \left ( x \right ) ={\frac {\sin \left ( x \right ) +2\,\ln \left ( \sin \left ( x \right ) -1 \right ) +{\it \_C1}}{\sec \left ( x \right ) +\tan \left ( x \right ) }} \right \} \]